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When you generate blue noise by shaping in the frequency domain and transforming, the samples are gaussian distributed, not uniform, as the author mentions. I w
by tlb 3y ago
When you generate blue noise by shaping in the frequency domain and transforming, the samples are gaussian distributed, not uniform, as the author mentions. I wonder if you can transform to a uniform distribution by sorting the samples, choosing 256 bins of equal size, then quantizing each pixel into those bins. That would be fast: O(n log n) in number or pixels.
Changing from gaussian to uniform is a distortion that presumably adds harmonics, but since they can only be higher frequencies than the original, the noise should still be blue.
- svantana 3y ago> but since they can only be higher frequencies than the original That's incorrect, distortion products spread both upwards and downwards in frequency. The easiest example to analyze is x^2, which corresponds to the spectrum convoluted with itself. From there it's easy to expand into polynomials. Anyway, what you're describing is pretty much a single step in a standard blue noise algo iteration.
- tlb 3y agoYou’re right. While a pure tone can only have higher harmonics when distorted, multiple tones can produce the difference frequency. And noise has every tone.
- FreeFull 3y agoEven when distorting a pure tone, the harmonics will reflect back down once they go past the Nyquist frequency.
- galangalalgol 3y agoAnd what happensnif you apply a high pass filter to white noise? That would have been my naive approach.
- cube2222 3y agoI believe the author acknowledges that a bit later. > The resulting noise is gaussian, not uniform. […] This is why you need a specialized algorithm. (The algorithm is afterwards described)